Proposal of a turbulent Prandtl number model for predicting heat transfer deterioration in supercritical flows

The supercritical heat transfer is characterized by abnormal heat transfer modes due to significant variation in thermophysical properties near the pseudocritical temperature. The sharp difference in the density sets up strong buoyancy forces, especially in vertical flows, causing severe heat transfer deterioration (HTD). The prediction of the onset of this HTD and wall temperature peaks is overpredicted with the existing Reynolds-averaged Navier–Stokes (RANS) models, where the turbulent Prandtl number is taken as a constant. The upward flow of supercritical fluids, viz., water, carbon dioxide, and n-decane, through circular pipes undergoing HTD is considered in this study. The components of the turbulent Prandtl number are analyzed to determine the effect of the variable turbulent Prandtl number model on predicting the peak wall temperature and its position, and to understand its impact on the heat transfer behavior. The increase in turbulent Prandtl number in the buffer region tends to suppress turbulence near the wall and improves the HTD, thus acting as a correction factor for RANS models in predicting the onset of HTD at supercritical conditions. Compared with available experimental data, the results improve significantly with the variable turbulent Prandtl number model, with a maximum error of 9.5%. The buoyancy production models are also varied for different cases, and their influence on turbulent heat flux calculation is compared with that of the variable Prt model.